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Discordance Detection in Regional Ordinance: Ontology-based Verification Shingo Hagiwara([email protected]) School of Information and Science Japan Advanced Institute of Science and Technology January 29, 2007 1 Aim of the Project cal items which includes negative prefixes as ‘un-,’ ‘dis-,’ ‘in-,’ and so on cannot coexist with their original positive words. Also, there are antonyms that have conflictive meanings without prefixes, as ‘liquid’ and ‘solid,’ or ‘vice’ and ‘virtue.’ Furthermore, some situations are incompatible with each other, which we can easily know by our common sense. For example, ‘submission with signature’ is incompatible with ‘electric submission.’ Then, we would like to rely on the notion of conflict [1] where the opposition of antonyms or negatively prefixed words are represented. In this paper, we propose a procedure of discordance detection in an actual legal code, that is the regional ordinance of Toyama Prefecture, Japan. In this study, we expand the notion of inconsistency to the discordance including antonyms based on an ontology, and precluded the conventional negative connective. We have implemented the system that converts XML logical formats to Prolog, and has inspected the whole code. 2 Approach and Idea Definition 2.1 Let be inconsistency, be propositional variables. . Then, and are in conflict. 2.1 Discordance The logical inconsistency becomes apparent only when appear in a set of propositions. Howboth of and ever, the inconsistency may not be seen from the superficial sentences of the legal code. To clarify such latent inconsistency, we need to supply some premises of the rules ( ). Then, we can derive inconsistency as . Therefore, we can regard such a part as discordance. In addition, there might be a loop of implications. For example, in a database where is the logical truth, we cannot collect the evidences of . In verification of discordance, we use a definition of inconsistency as follows. However, if we were to define conflicts, we must enumerate all the possible combinations of predicates which appear in a legal code, where the number of pairs would be ¾ . To avoid this problem, we employ an ordersorted hierarchy of ontology. 2.3 Conceptual Conflict Next, we consider a concept of conflict in order-sorted logic. First, we introduce (meet) operation that returns the infimum (the greatest lower bound) with regard to ‘ ’, taking two sorts [2]. 2.2 Conflict Definition 2.2 exclusive relation Let be sorts and be the minimum sort. Then, The discrepancy or the discordance is not only the logical inconsistency. In the lexicon of legal code, such lexi- 1 Rules of the law Ontology XML (FOL and OWL) Converter Knowledgebase of the law Ordered sorts Validation Code for Execution Prolog 4 Validator Conflict Result Loop Result We employed Gabbay’s conflict instead of the conventional negative connective. Thus, we could employ ordered sorted hierarchy in ontology to detect incompatible notions. We have implemented a discordance detection system based on the logical format of XML, where those XML files were converted into Prolog, and the verification program scans the code to detect discordance. Future Direction Our future target would be the handling of ‘’. We simply divided those rules including disjunctions to implement them in Horn clause. However, we need to consider the computational efficiency. Also the input format of our system is XML based on first order logic (FOL). Translating natural language sentences into FOL still remains a tough problem. Text data Figure 1: Overview of Implementation As stated above, the exclusive relation can express the conflict on ordered sorts. An ontology consists of tree-structured hypernymhyponym relations, together with extraneous knowledge base. In this study, we regard an ontology as a ordered sort. Therefore, we extract conceptual conflicts from an ontology with the above definition. 5 2.4 Implementation Shingo Hagiwara and Satoshi Tojo. Discordance detection in regional ordinance: Ontology-based validation. In Legal Knowledge and Information Systems JURIX, Pariss, 2006. JURIX, IOS Press. Shingo Hagiwara, Mikito Kobayashi, and Satoshi Tojo. Belief updating by communication channel. In Seventh Workshop on Computational Logic in Multi-Agent Systems (CLIMA-VII), 2006. (Revised Selected and Invited Papers, volume 4371 of Lecture Notes in Computer Science. Springer, 2006). we explain our implementation which consists of two programs. Its overview is Figure. 1. In the figure, one of the programs is a converter, written in Ruby, and the role is conversion of XML files into Prolog code. Another one is a validator, written in Prolog, and the role of which is validation of the code output by the converter. References [1] Dov M. Gabbay and A. Hunter. Negation and contradiction. In Dov Gabbay and Heinrich Wansing, editors, What is Negation?, pages 89–100. Kluwer Publishers, 1999. 3 Progress of 2006 Publication in 2006(after April) [2] K. Kaneiwa and S. Tojo. An order-sorted resolution with implicitly negative sorts. In International Conference on Logic Programming, pages 300–314. Cyprus, 2001. We have targeted the real problem of ordinance revision held in Toyama prefecture in 2002, instead of artificial toy problem. 2